A statistics-based threshold for the RMS-energy oscillation detector
Introduction
To ensure reliable power system operation, oscillatory grid behaviors must be effectively monitored and addressed. Oscillations arise in power systems for a variety of reasons. Inter-area electromechanical oscillations between groups of generators are always present in large power systems but can have severe consequences when poorly damped [1]. Forced oscillations, which are often caused by equipment malfunction or misoperation, can also threaten power system reliability under certain circumstances [2].
Over the past several years, the deployment of phasor measurement unit (PMU) networks in electric power systems has provided utilities with improved visibility of oscillatory grid behaviors. Significant research has led to the development of several methods to detect oscillations and support utilities in addressing them. Early synchrophasor-based analysis methods were designed to track the frequency and damping ratio of inter-area electromechanical modes of oscillation using the principles established in [3]. Continued analysis of synchrophasor measurements revealed the presence of forced oscillations, and eventually led to the conclusion that forced oscillations are much more prevalent than sustained modal oscillations [4]. This finding shifted interest from methods that track modes of oscillation during ambient conditions to those that detect the onset of sustained oscillations. A survey of detectors specifically designed for forced oscillations is provided in [5]. Generic methods able to detect any type of sustained oscillation are presented in [6], [7], [8] (also see the discussion of the Fast SubSpace Identification (FSSI) method [9] as presented in [10]).
These detectors operate by comparing a metric derived from synchrophasor measurements to a detection threshold. In some cases, authors have provided explicit guidance on setting the threshold. For example, the method proposed in [11] is based on spectral coherence and uses bootstrapping to select detection thresholds with a user-specified probability of false alarm. Similarly, statistical detection theory was used to limit false alarms in detectors based on the periodogram [12], [13] and multitaper [14] spectral estimators. In the absence of theoretical results, practitioners must depend on extensive offline studies and experience to establish thresholds.
At present, this is the case with the root-mean-square (RMS) energy detector [8], which is one of the few methods proposed in the literature that is deployed by utilities and reliability coordinators [15], [10]. In this method, filtering is used to isolate frequency bands and estimate the resulting signal’s RMS-energy. When the energy exceeds a threshold for a certain amount of time, an oscillation is detected. This method is an extension of an approach that monitors the envelope of the input signal [16]. The authors of [17] also extended the work in [16] for use in sub-synchronous oscillation detection.
Presently, the thresholds for RMS-energy detectors are determined with baselining studies and experience because analytical expressions are unavailable. Baselining studies are intensive, requiring examination of large amounts of historical data for every input signal. Resulting thresholds are based largely on engineering judgment and may vary significantly between organizations that need to coordinate during system-wide events. The theoretical work in this paper simplifies the process of setting detection thresholds for RMS-energy detectors. Rather than proposing a new detector, this paper focuses on theoretical developments to support and enhance the RMS-energy method already widely accepted by industry.
The key contributions of this paper are (1) a novel expression for a statistics-based oscillation detection threshold for RMS-energy detectors and (2) three methods for calculating the threshold based on synchrophasor measurements. Each of the three methods has a distinct advantage, and together they ensure that the threshold can be calculated reliably for various applications. The threshold is derived using the relationship between the RMS-energy and the discrete Fourier transform (DFT), which has known statistical properties. Through the use of statistics, the threshold is expressed in terms of the detector’s probability of false alarm, which allows users to adjust the detector’s performance with predictable outcomes.
The rest of the paper is organized as follows. Background on the RMS-energy detector’s theory and implementation is provided in Section 2. The new expression for the detector’s threshold is then derived in Section 3. Theory for calculating the threshold is established in Section 4, followed by overviews and discussion of the three methods in Section 5. Results from simulation and measurement-based tests are provided in Section 6. Concluding remarks are provided in Section 7.
Section snippets
Background on RMS-energy detectors
The thresholds proposed in this paper are designed for use with the oscillation detector described in [8]. While general design principles were described in [8], the explicit filter designs were not specified. This section provides an overview of the RMS-energy detector’s operation, but it also specifies filters very similar to those in [8] to make the research reproducible and more accessible for those wanting to implement the proposed methods.
The detection module described in [8] is composed
Deriving an expression for the detection threshold
Consider the band-pass filtered signal at the output of Fig. 1. For a window of length N, the RMS of this signal is given byIn [8], the RMS is approximated by a moving average filter (see Fig. 2) and then compared to a threshold to determine if an oscillation is present. Using terminology from the statistical signal processing literature, the RMS is serving as a test statistic [20]. If information about the statistical distribution of a test statistic is known, it can be
Methods for calculating the detection threshold
Calculating the detection threshold in (17) is not difficult, but obtaining the distribution’s parameters requires care. In this section, methods to obtain these parameters are proposed. The most direct method is first described in Section 4.1. A potential pitfall of this method motivates the use of an alternative set of parameters, as described in Section 4.2. Two approaches to calculating these alternative parameters are described in Section 4.3.
Implementation considerations
Sections 3 Deriving an expression for the detection threshold, 4 Methods for calculating the detection threshold established the theory necessary to calculate thresholds for RMS-energy oscillation detectors with an associated probability of false alarm. This theory leads to multiple options for implementation. In this section, these options are restated for clarity along with each approach’s advantages and disadvantages. As will be demonstrated in Section 6, all implementation options result in
Results
The proposed methods were tested with simulation data to validate theoretical results and with field-measured data to demonstrate practical viability. Filter design was carried out in MATLAB using the specifications in Table 1, Table 2, Table 3, Table 4, which are based on the impulse- and frequency-response plots in [8]. Frequency measurements were used as inputs to the detectors. When calculating thresholds, 30-min windows of data were used. Because the threshold calculation involves
Conclusion
The widespread deployment of synchrophasor networks has enabled utilities to perform effective oscillation detection. RMS-energy oscillation detectors have been implemented by the electric industry, but detection thresholds are currently determined based on time consuming baselining studies and engineering judgment. In this paper, an expression for a statistics-based detection threshold is derived. This expression allows the user to tune the probability of false alarm to adjust the detector’s
CRediT authorship contribution statement
Jim Follum: Conceptualization, Methodology, Investigation, Writing - original draft, Visualization. Jesse Holzer: Methodology, Writing - review & editing. Pavel Etingov: Project administration, Funding acquisition, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The authors would like to thank the Bonneville Power Administration (BPA) for providing real-world measurements to validate the approaches. The authors are also grateful to Daniel Trudnowski of Montana Tech for use of the miniWECC model.
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The Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by Battelle Memorial Institute under Contract DE-AC05-76RL01830.